1. Pre-Algebra 12-8 Inverse Variation Learn to recognize inverse variation by graphing tables of data.

2. Pre-Algebra 12-8 Inverse Variation An inverse variation is a relationship in which one variable quantity increases as another variable quantity decreases. The product of the variables is a constant. xy = 120 xy = k kxkx y =y = 120 x y =y = INVERSE VARIATION WordsNumbersAlgebra

3. Pre-Algebra 12-8 Inverse Variation Tell whether the relationship is an inverse variation. A. The table shows how 24 cookies can be divided equally among different numbers of students. Additional Example 1A: Identify Inverse Variation Number of Students 23468 Number of Cookies 128643 2(12) = 24; 3(8) = 24; 4(6) = 24; 6(4) = 24; 8(3) = 24 xy = 24 The product is always the same. The relationship is an inverse variation: y =. 24 x

4. Pre-Algebra 12-8 Inverse Variation Tell whether each relationship is an inverse variation. B. The table shows the number of cookies that have been baked at different times. Additional Example 1B: Identify Inverse Variation Number of Students 1224364860 Time (min) 1530456075 12(15) = 180; 24(30) = 720 The relationship is not an inverse variation. The product is not always the same.

5. Pre-Algebra 12-8 Inverse Variation Tell whether the relationship is an inverse variation. A. Try This: Example 1A x 3020151210 y 23456 30(2) = 60; 20(3) = 60; 15(4) = 60; 12(5) = 60; 10(6) = 60 xy = 60 The relationship is an inverse variation: y =. 60 x The product is always the same.

6. Pre-Algebra 12-8 Inverse Variation Tell whether the relationship is an inverse variation. B. Try This: Example 1B x 24812 y 42186 2(4) = 8; 2(6) = 12 The relationship is not an inverse variation. The product is not always the same.

7. Pre-Algebra 12-8 Inverse Variation Additional Example 2A: Graphing Inverse Variations Graph the inverse variation function. A. f(x) = 4 x xy –4 –2 –1 1 2 4 – 12 –1 –2 –4 –8 8 4 2 1

8. Pre-Algebra 12-8 Inverse Variation Graph the inverse variation function. B. f(x) = Additional Example 2B: Graphing Inverse Variations –1 x xy –3 –2 –1 1 2 3 – 12 1313 1 2 –2 –1 1 2 – 1 3 –

9. Pre-Algebra 12-8 Inverse Variation Try This: Example 2A xy –4 –2 –1 1 2 4 – 12 1 2 4 8 –8 –4 –2 –1 Graph the inverse variation function. A. f(x) = – 4 x

10. Pre-Algebra 12-8 Inverse Variation Try This: Example 2B Graph the inverse variation function. B. f(x) = 8 x xy –8 –4 –2 –1 1 2 4 8 –2 –4 –8 8 4 2 1

11. Pre-Algebra 12-8 Inverse Variation As the pressure on the gas in a balloon changes, the volume of the gas changes. Find the inverse variation function and use it to find the resulting volume when the pressure is 30 lb/in 2. Additional Example 3: Application Volume of Gas by Pressure on Gas Pressure (lb/in 2 )5101520 Volume (in 3 )30015010075 You can see from the table that xy = 5(300) = 1500, so y =. 1500 x If the pressure on the gas is 30 lb/in 2, then the volume of the gas will be y = 1500 ÷ 30 = 50 in 3.

12. Pre-Algebra 12-8 Inverse Variation Try This: Example 3 An eighth grade class is renting a bus for a field trip. The more students participating, the less each student will have to pay. Find the inverse variation function, and use it to find the amount of money each student will have to pay if 50 students participate. Number of Students by Cost per Student Students10202540 Cost per student201085 You can see from the table that xy = 10(20) = 200, so y =. 200 x If 50 students go on the field trip, the price per student will be y = 200  50 = $4.